Abstract.
We prove that for any weighted backward shift B = B w on an infinite dimensional separable Hilbert space H whose weight sequence w = (w n ) satisfies \( \sup_{n} {\left| {w_{1} w_{2} \ldots w_{n} } \right|} = \infty \), the conjugate operator \( C_{B} :S \mapsto BSB^{*} \) is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an \( S \in S(H) \) such that \( \{ C^{n}_{B} (S) = B^{n} SB^{*n}\} _{{n \geq 0}} \) is dense in S(H). We generalize the result to more general conjugate maps \( S \mapsto TST^{*} \), and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Petersson, H. Hypercyclic Conjugate Operators. Integr. equ. oper. theory 57, 413–423 (2007). https://doi.org/10.1007/s00020-006-1459-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00020-006-1459-8